Monthly Archives: November 2012

A gambler has just lost all but one $1 in Vegas and decides to go for a walk. Unfortunately he gets hit by a bus but, having lived mostly a good life aside from the gambling, is shown God’s mercy and lands in heaven. They only have one type of gambling in heaven, it is a simple choice-free game with the following rules:

A coin is tossed. If it comes up tails, you lose $1. If it comes up heads, your entire bankroll is tripled.

The gambler only has the $1 he had on him when he died (turns out you keep your money when you go to heaven). Here is a possible outcome of his playing this game:

$1 – H -> $3

$3 – T -> $2

$2 – H -> $6

$6 – T -> $5

$5 – T -> $4

$4 – T -> $3

$3 – T -> $2

$2 – T -> $1

$1 – T -> $0

And thus he is broke.

The question is this: starting with his $1, what is the probability he will live the rest of eternity broke in heaven? The alternative, presumably, is that he spends eternity doing what he loves most: gambling. Do all paths eventually lead to bankruptcy a la Gambler’s ruin, or is there a nonzero probability of playing forever?

You may leave your ideas in the comments, and I will post a solution in a few days.